Ms Gillard said the commission would address "institutional responses to child abuse" - the instances of abuse as well as the manner in which they have been dealt - by a range of institutions.

She said she would work in coming weeks with Attorney General Nicola Roxon to define the terms of reference, but said she imagined the investigation would go back decades.

The announcement follows calls by the Greens and some Labor backbenchers for a Royal Commission into abuse in the Catholic Church, after it was alleged by a senior policeman that investigations were hindered and in some cases compromised by church officials.

Detective Chief Inspector Peter Fox whose revelations over the alleged cover up sparked a public outcry over the weekend was speaking with ABC Radio as the Prime Minister made the announcement. He said that he was "stunned that it's happened so quickly, and delighted, absolutely delighted for all those victims out there."

He added that he had been overwhelmed by public support since speaking out, and that he was hopeful the Royal Commission would provide "opportunity to get things right, to look at recommendations for laws that should be changed to protect kids, or systems to be put in place."

Ms Gillard stressed the inquiry would not be limited to the Catholic Church.

"We will work on the specific terms of reference but this is about children who were in the care of religious organisations - so that's all religious organisations - it's about children who were in state care, it's about children who were in the care of not-for-profit bodies other than religious organisations, it will therefore go as well to the response of children's services agencies, and the response of the police."

"The allegations that have come to light recently about child sexual abuse have been heartbreaking," Ms Gillard said.

"These are insidious, evil acts to which no child should be subject. The individuals concerned deserve the most thorough of investigations into the wrongs that have been committed against them.

"They deserve to have their voices heard and their claims investigated. I believe a Royal Commission is the best way to do this."

Opposition Leader Tony Abbott had earlier given his backing to a Royal Commission, provided it was not limited to the Catholic Church.

"Any investigation must be wide-ranging, must consider any evidence of the abuse of children in Australia, and should not be limited to examination of any one institution. It must include all organisations, government and non-government, where there is evidence of sexual abuse."

Ms Gillard said terms of reference and a proposed commissioner would be submitted soon to Governor-General Quentin Bryce, who has the power to establish the commission.

She said she had the backing of her Cabinet. She will speak in coming days to state premiers about co-ordinating with any existing inquiries.

The Prime Minister would not be drawn on either the cost or the timeframe of the Royal Commission saying that "the time should be taken to get it right, to make sure that the royal commission does the work that we want it to do."

"In terms of costs, the government will make appropriate provision for them and the matter will be accounted for in the budget in May next year. Clearly, the costs will become apparent as the inquiry goes on and the government will make continuous provision as necessary."